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Progress in null canonical gravity in terms of free initial data

The talk will focus on issues connected with the quantization of initial data for vacuum general relativity on null hypersurfaces. Complete and constraint free initial data for GR can be given on pairs of intersecting null hypersurfaces. These offer a route to a canonical quantization of GR which avoids having to deal with constraints. However the Poisson algebra of these data is rather intricate and it is not obvious how one might quantize it. This algebra is however almost the same in the cylindrically symmetric case as in the full theory, which suggests that the cylindrically symmetric theory ought to offer valuable insights. Here I present recent joint work with Javier Peraza and Miguel Paternain relating the Poisson algebra in the cylindrically symmetric case to well studied algebraic structures.